0:00
Hi there.
00:01
So for this problem, the expression that describes this dump is that y is equal to 0 .6 times x to the 4.
00:14
And the other information that this is below the line y is equal to 160.
00:21
And the water level is 28 meters below the top of the dam.
00:26
So we need to find the force exerted on the dam by the water pressure.
00:30
That's what we need to obtain the force.
00:33
Now, first of all, we start by knowing that the pressure in a fluid is equal to the density times the acceleration due to gravity times the height, where row is the density, of course, g is the acceleration due to gravity, and h is the height of the fluid, or the death of this fluid.
00:56
Now, the height can be found by subtracting the height of the dam, from the base that we're going to call y of x from the surface height.
01:07
So that will be the value that we are given of the 160 minus the 28 meters.
01:17
So from this we obtain a value of 132.
01:27
Okay, so now the height function is therefore, let's call it it is equal to 132, this minus 0 .0 .6 times adds to the 4.
01:49
Now, the pressure force is related to the pressure p by just, well, let's divide this by c because this is going to be the pressure per meter in this case.
02:03
It's just a product between d pressure and x, where x is the distance at the death edge x, h of x.
02:15
Now, so, but in this case, since the distance is changing, what we need to do is the integral of the pressure integrated over x.
02:29
Now, first of all, we know we also need to determine the limits of integration.
02:34
Now, we know that the minimum value for x is equal to zero, and the maximum value, we can obtain that from here, from this expression.
02:46
So what we need to do is to just simply set that expression equal to 132 and solve for x.
02:55
So that will be that x is equal to the fourth root of, um, 132 divided by 0 .6 and we take that.
03:13
So let me just use my calculator.
03:19
We obtain a value of 3...